Separation of ionic mixtures and characterization of ions in the gas phase using ion mobility techniques has become common in analytical chemistry. The key advantage of gas-phase separations over condensed-phase methods is exceptional speed allowed by rapid molecular motion in gases. Since their first demonstration a decade ago, instrumental platforms combining ESI or MALDI soft-ionization sources, ion mobility separations, and mass-spectrometry (MS) have undergone a sustained development that has improved their resolution and sensitivity to the levels demanded by practical applications. Commercial introduction of such systems is accelerating the adoption of combined ion mobility/mass spectrometry (MS) as a mainstream analytical paradigm, in particular for complex biological samples such as proteolytic digests and mixtures of lipids, nucleotides, or metabolites.
Ion mobility spectrometry (IMS) has been known since the 1970's. In IMS, ions drift through a non-reactive buffer gas under the influence of a modest electric field, wherein the drift velocity (ν) in the field having intensity E is determined by a quantity known as ion mobility (K) according to equation [1]:ν=K(E)  [1]Measured mobilities are normally converted to reduced values (K0) by adjusting the buffer gas temperature (T, Kelvin) and pressure (P, Torr) to standard (STP) conditions, via equation [2]:K0=K(P/760)×(273.15/T)  [2]The mobility of an ion always depends on the electric field and may be expressed as an infinite series of even powers over (E/N), where N is the gas number density, by the series expansion of equation [3]:K(E/N)=K(0)[1+a(E/N)2+b(E/N)4+c(E/N)6+d(E/N)8+. . . aj(E/N)2j]  [3]
IMS measures K(E/N) at a particular E/N. However, over an experimentally relevant range of E/N, e.g., from 0 to ˜100 Td, K(E/N) varies by a few percent at most, except for some monatomic and other small ions. Thus, though K(E/N) could be revealed by high-field IMS measurements at low pressure P, in practice, IMS separates ion mixtures by zero-field mobility K(0). Separation, characterization, or identification of ions is based on coefficients with the terms of the series expansion: aj. The mobility of an ion is related to its size and mass m, especially within classes of homologous or chemically/structurally similar species. The correlation between ion mobility and mass means a limited orthogonality between IMS and MS analyses. For example, ions of the same charge state z follow certain trend lines in 2-D IMS/MS plots depending on chemical composition and compound type. Trend lines are described in the art for atomic nanoclusters (including carbon, semiconductor, and metal species) and biomolecules (including peptides, lipids, and nucleotides). In ESI, complex biological analytes such as tryptic digests generally yield ions with a distribution of “z” that have different trend lines in IMS/MS space. While this improves the orthogonality between IMS and MS and thus increases the 2-D IMS/MS peak capacity, the correlation between ion mobility and mass remains a fundamental limitation of IMS/MS methodology.
Field asymmetric waveform ion mobility spectrometry (FAIMS) is another method to separate ions based on their transport properties in gases. FAIMS separation is based not on the absolute mobility, but the difference between K at high and low E. A FAIMS separation may be achieved by a periodic time-dependent electric field E(t) that meets the conditions of equation [4] with respect to integrals over period Δt:∫E(t)dt=0; ∫E3(t)dt≠0  [4]An E(t) subject to condition [4] cancels the effect on ion motion provided by the first but not higher terms of polynomial [3]. The higher terms result in a net motion of ions through gas with mean velocity equal to
                              〈          v          〉                =                                            (                                                ∫                                      t                    0                                                                              t                      0                                        +                                          Δ                      ⁢                                                                                          ⁢                      t                                                                      ⁢                                                      K                    ⁡                                          (                      E                      )                                                        ⁢                                      E                    ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                                      ⅆ                    t                                                              )                        /            Δ                    ⁢                                          ⁢          t                                    [        5        ]            which for K(E), given by equation [4], expands into equation [6]:<v>=K(0)×[∫E(t)dt+(a/N2)∫E3(t)dt+(b/N4)∫E5(t)dt+(c/N6)∫E7(t)dt+(d/N8)∫E9(t)dt+(e/N10)∫E11(t)dt]/Δt  [6]
The motion may be offset by a drift with velocity vC due to constant “compensation field” EC defined by equation [7]:vC≈EC×K(0)  [7]:with EC dependent on the ion and the buffer gas and calculated via equation [8]:EC≈[(a/N2)∫E3(t)dt+(b/N4)∫E5(t)dt+(c/N6)∫E7(t)dt+(d/N8)∫E9(t)dt+(e/N10)∫(E11)(t)dt+ . . . ]/Δt,  [8]
By equation [8], independence of EC of K(0) allows FAIMS to disperse ions by the sum of the second and further terms of equation [3] regardless of the absolute mobility. At a sufficiently low peak amplitude of E(t), known as the “dispersion field” (ED), EC is mostly determined by a, the coefficient with the leading term of equation [8]. Subsequent terms (especially the 2nd term) affect the FAIMS response at higher ED, which in some cases allows measuring the coefficient b. Still, FAIMS separations are primarily controlled by the value of a, and differences between further coefficients do no create a significant orthogonality and so are of little analytical utility.
The condition in equation [4] may be satisfied by an infinite number of E(t) functions. However, FAIMS performance is optimized by maximizing <v>∝∫E3(t)dt/Δt (ignoring higher-order terms in equation [6]). This condition is ideally achieved by a “rectangular” waveform, where E(t) switches between segments of “high field” (ED) applied over a time tD and low field (EL) in the opposite direction applied over a time tL. The criterion ∫E(t)dt=0 of condition [4] requires ED/EL=−tL/tD. That quantity (known as the “high-to-low” ratio f) may mathematically vary between 1 and +∝, but the best FAIMS performance is provided by f=2, producing equation [9]:E(t)=ED{tε[0; t/3]}; E(t)=−ED/2{tε[Δt/3; Δt]},  [9]with <v> and EC defined by equations [10] and [11]:<v>=K(0)[(a/N2)ED3/4+5(b/N4)ED5/16+ō(cED7/N6)]/Δt  [10]EC=[(a/N2)ED3/4+5(b/N4)ED5/16+ō(cED7/N6)]/Δt  [11]
Waveforms defined by equation [9] and corresponding model ion trajectories are plotted in FIG. 1a and, for the inverted E(t) polarity, in FIG. 1b. Calculations do not account for ion diffusion or space-charge effects, which is proper for the purpose of comparing trajectories induced by different E(t). The E(t) form influences the diffusion only slightly through high-field and anisotropic terms and does not affect Coulomb repulsion. Commercial FAIMS analyzers use not the ideal E(t) of equation [9], but its approximation, by either a bisinusoidal (a sum of two harmonics) or a clipped, displaced sinusoidal waveform. Substitution of these waveforms for the rectangular E(t) sacrifices some resolution and/or sensitivity but simplifies engineering substantially.
In practice, FAIMS analyses involve pulling an ion beam through a gap between two electrodes (the so-called “analytical gap”) by a gas flow or weak electric field along the gap. A voltage waveform applied to this electrode pair creates the field [E(t)+EC] across the gap. Parallel planar, coaxial cylindrical, and concentric spherical electrode geometries (and their combinations) are known in the art. At any given EC, ideally only one species with K(E) yielding <v>=vC is balanced in the gap and may pass. Other ions drift across the gap and are eventually neutralized on an electrode. A spectrum of an ionic mixture may be produced by scanning EC.
Equation [3] indicates that a differential IMS effect (for any n) should, in principle, exist at any E. However, the FAIMS resolution depends on <v> that scales with ED3 by equation [10], and in practice, separation becomes useful at ED/N ˜40-50 Td, with optimum performance achieved at ˜65-80 Td.
Fundamentally, the value of “a” is not related to m as closely as K(0). In particular, “a” may be both positive and negative, while K is always positive. Hence FAIMS is, in general, more orthogonal to MS than IMS. That deduction has broad experimental support, e.g., for tryptic peptide ions, FAIMS and MS separations are virtually independent, but IMS and MS are substantially correlated. This is a major advantage of FAIMS/MS over IMS/MS.
A successful development of FAIMS prompts the question whether further conceptually new separation approaches based on ion transport in gases might exist. To be useful, those approaches must exhibit a substantial orthogonality to both FAIMS and IMS or outperform them in other respects. There remains a need for novel separation approaches and devices providing high resolution and sensitivity, and significant orthogonality to known IMS and FAIMS separations, as well as to MS.